I have heard multiple estimates on the quantity of stars within our galaxy, anything from 100 to 400 billion of them. The estimates seem to be increasing for the time being. What are the main methods that are used to make these estimates, and why are there such large discrepancies between them?

2 Answers
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The estimates I've read are similar to yours: 200 to 400 billion stars. Counting the stars in the galaxy is inherently difficult because, well, we can't see all of them.

We don't really count the stars, though. That would take ages: instead we measure the orbit of the stars we can see. By doing this, we find the angular velocity of the stars and can determine the mass of the Milky Way.

But the mass isn't all stars. It's also dust, gas, planets, Volvos, and most overwhelmingly: dark matter. By observing the angular momentum and density of stars in other galaxies, we can estimate just how much of our own galaxy's mass is dark matter. That number is close to 90%. So we subtract that away from the mass, and the rest is stars (other objects are more-or-less insignificant at this level).

The mass alone doesn't give us a count though. We have to know about how much each star weighs, and that varies a lot. So we have to class different types of stars, and figure out how many of each are around us. We can extrapolate that number and turn the mass into the number of stars.

Obviously, there's a lot of error in this method: it's hard to measure the orbit of stars around the galactic center because they move really, really slowly. So we don't know exactly how much the Milky Way weighs, and figuring out how much of that is dark matter is even worse. We can't even see dark matter, and we don't really understand it either. Extrapolating the concentrations of different classes of stars is inexact, and at best we can look at other galaxies to confirm that the far side of the Milky Way is probably the same as this one. Multiply all those inaccuracies together and you get a range on the order of 200 billion.

Good answer. In short: we look at a small sample of the Milky Way near us and figure out how many stars it has and how much it weighs, then we figure out how much the whole galaxy weighs, and we estimate from there.
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WedgeJun 5 '11 at 10:15

The estimate of the dark matter contribution is only necessary in so far that you need a model for Galactic potential in order to come up with a self consistent model for the density distribution of the stars.
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Rob JeffriesDec 3 '14 at 10:53

I've added this because I don't think the accepted answer is very clear.

Estimating the number of stars in the Galaxy relies mostly on two things.

We estimate the present day mass function (that is the number of stars that exist per unit mass per unit volume) in the solar neighbourhood.

We construct a model for the overall density distribution of the stars in our Galaxy and assume that this is governed by the same mass function.

The presence or not of dark matter is almost totally irrelevant, except that it can be of help in constructing self-consistent density models of the Galaxy that match the dynamics of stars. What is much more helpful is very detailed censuses of stars carried out in different directions that have good estimates for the distances of the stars that are counted and can take account of the ubiquitous obscuration by dust that is a problem in almost every direction except straight out of the Galaxy plane. A further problem is that it turns out that the stars that dominate the Galactic population are very faint stars of about $0.25M_{\odot}$. These cannot be seen beyond a few hundred pc, so estimates of stellar numbers are a vast extrapolation based on what we observe in a very small volume around the Sun. We are crucially reliant on the assumption that the low-mass stellar mass function is invariant - and this is very hard to test.